Periodic planewave and molecular cluster density functional theory (DFT) calculations were performed on Iα and Iβ cellulose in four different conformations each. The results are consistent with the previous interpretation of experimental X-ray and neutron diffraction data that both Iα and Iβ cellulose are dominantly found in the tg conformation of the hydroxymethyl group with a H-bonding conformation termed “Network A”. Structural and energetic results of the periodic DFT calculations with dispersion corrections (DFT-D2) are consistent with observation suggesting that this methodology is accurate to within a few percent for modeling cellulose. The structural and energetic results were confirmed by comparison of calculated vibrational frequencies against observed infrared and Raman frequencies of Iα and Iβ cellulose. Structures extracted from the periodic DFT-D2 energy minimizations were used to calculate the 13C nuclear magnetic resonance chemical shifts (δ13C), and the tg/Network A conformations of both Iα and Iβ cellulose produced excellent correlations with observed δ13C values.